Linear extensions, projections, and split faces

AbstractThe main result is essentially: Let F be a closed split face of a compact convex set K such that A(F) is separable and has the (positive) metric approximation property. Then there is a (positive) linear extension operator from A(F) into A(K) of norm one.This is applied to C∗-algebras thus giving sufficient conditions for the existence of right inverses to surjective ∗-homomorphisms